# Decision Tree

The decision tree is one of the basic tools and keys for the project manager in each decision-making process. It is considered a sound and logical way that leads to the selection of the proper decision. Recently, I considered that a person who does not know how to use a decision-making tree is a person living in an isolated cave. Here is proof that this method is the most common way.

The decision tree method is based on the probability of A, B, and C occurring and is calculated by:

Ps = P, XP„XPc

 Figure 3.19 Probability theory.

This probability is presented in Figure (3.19). The probability of three events, A, B, and C, occurring at the same time will be presented by the intersection portion from the circle.

The core definition of risk is the probability of the event occur­ring multiplied by the output of this event: Risk Assessment = probability x consequence.

To explain the decision tree, let’s use dice and assume that the first player to throw the dice will earn 6,000 pounds only if the result is a 6, but if it is another number, the player will lose the 1,000 pounds, and the expected value calculation will be as follows.

The possible emergence of a 6 is the probability of 1/6, so the expected value equation is as follows:

Expected Value = (1 / 6) X 6000 – (5 / 6) X 1000 = 166.7

The general equation, a difference of products, is as follows:

EV = P XC-PfXC„

s s / f

where Ps and Pf are the probability of success and probability of failure, respectively. Cs and Q are the consequence in case of success and failure, respectively.

We find that the probability of rolling a 6 is the one-sixth, but the expected value of the payout is 166.7 pounds, which is greater than zero (the expected value of risk). A high expected value indicates that the risk is better. Therefore, when compared with the display of the other player, our player found the expected value greater.

This concept is the main decision-making tool that you would use if you had more than one project and you want to choose one of these projects. Therefore, it is important to be aware of calculating the prob­ability of success of each project as well as the value of that success.

Therefore, in applying the decision tree method to solve an engi­neering problem, or in the feasibility study, one must specify the expected outcomes and possibility of solving the engineering prob­lem. This will determine the likelihood of success. The focus should be to identify all the different ways to determine the likelihood of the event because it depends entirely on the experience from start to finish. Therefore, the experience is the key factor to the success of this method and can simply explain the manner of the following example.

This example of Proverbs is common in the case of decisions in engineering projects for the oil industry. You can imagine that all the decisions of drilling for oil depend on the possibility and existence of oil in the ground, and the volume of the amount of ground reservoir varies from a large reservoir to a medium and to a small. Therefore, decision makers should use the decision tree to determine whether the drilling work will do or not.

Figure (3.20) is a case study on making the decision to drill or not. If you drill, you have 2 possible outcomes – that the well will be dry or that the well will have oil.

If you have an oil reserve, you have three possible outcomes. The reserve may be high, low, or medium. Every outcome has its probability of occurrence. It is noted from the figure that the total probability is equal to one, based on the probability theory. In each scenario of outcomes, calculate the present value (PV).

By multiplying the probability with the present value (PV), one will obtain the expected value (EV). By adding all the values, you get the expected value of the project which in this case is 4.6 million dollars. Therefore, this project would have less expected value than a project somewhere else that might be worth more than 4.6 million dollars, and a decision could be made.

 p x pv = EPV Figure 3.20 Case study one.

 Figure 3.21 Case study two.

For example, if you find that your investment in a country gives the expected value of 8 million dollars, will you invest in any of the two countries? Naturally, you will not invest in the site in the example, but your decision will be clear that you will invest in the country that will give higher weight to the expected value of invested money.

Using the decision tree, potential problems you may encounter during the implementation of a project can be obvious, and this is evidenced by the following example in Figure (3.21), which is the same as the previous example with the possible delays in drilling wells. This usually happens in some countries that permit administrative bureaucracy where the delay is a result of admin­istrative work for foreigner permits and correspondence paper or the equipment for custom paper work. This is an example where the auger is not available, and this is something that will have an impact on the accounts of the present value of investment, as in the following example. It is clear that the number of decision-making trees depends primarily on the experience, as it considers all the possible problems that can be urged as well as prospects.

Figure (3.22) presents another example for constructing a new facility, and you may cancel this project or group through the appraise phase (conceptual design). The possible outcomes from the study are that you will need a plant or not. Due to production there are three possible outcomes: abandon the facility, make no modifications, or modify the facility.

The decision tree is very easy to use, but the problem is how to calculate the probability for every event. You can assume the probability value using your experience, but it will affect the result.

The best way to calculate this probability is by using the Monte – Carlo simulation technique. In every case, start by building

 Figure 3.22 Case study three.

a model for a reservoir in an oil and gas project, and define the mean, standard deviation, and the probability distribution that are present in the reservoir model as area, height, porosity and others parameters. At the same time, build the model for the present-value calculation, and also define the parameters for each variable.